Poisson Regression STA 2101442 Fall 2018 See last
- Slides: 5
Poisson Regression STA 2101/442 Fall 2018 See last slide for copyright information
Regression: Outcomes are Counts • Poisson process model roughly applies • Examples: Relationship of explanatory variables to – Number of children – Number of typos in a short document – Number of workplace accidents in a short time period – Number of marriages • For large λ, CLT says a normality assumption is okay, but not constant variance • Yes I know, we could stabilize the variance with a square root transformation.
Linear Model for log λ • • log λ = β 0 + β 1 x 1 + … + βp-1 xp-1 Implicitly for i = 1, …n Everybody in the sample has a different λ=λi Take exponential function of both sides Substitute into Poisson likelihood Maximum likelihood as usual Likelihood ratio tests, etc.
log λ = β 0 + β 1 x 1 + … + βp-1 xp-1 • Increase xk with everything else held constant, and – Log λ increases by βk – λ is multiplied by eβk
Copyright Information This slide show was prepared by Jerry Brunner, Department of Statistics, University of Toronto. It is licensed under a Creative Commons Attribution - Share. Alike 3. 0 Unported License. Use any part of it as you like and share the result freely. These Powerpoint slides are available from the course website: http: //www. utstat. toronto. edu/brunner/oldclass/appliedf 18
